Final answer:
The function with an inverse that is also a function is C. m(x) = -7x, since it is a linear function with a non-zero slope, passing the Horizontal Line Test.
Step-by-step explanation:
The question asks which function has an inverse that is also a function. To determine if a function has an inverse that is also a function, we can use the Horizontal Line Test. The test states that if any horizontal line intersects the graph of the original function at more than one point, then the function does not have an inverse that is also a function.
A. b(x) = x2 + 3 - This function does not have an inverse that is a function because it fails the Horizontal Line Test; its graph is a parabola that opens upwards, so horizontal lines intersect the graph at more than one point.
B. d(x) = –9 - This is a horizontal line, which fails the Horizontal Line Test; any horizontal line (other than d(x) itself) does not intersect the graph, so there's no inverse function.
C. m(x) = –7x - This function has an inverse that is also a function because it passes the Horizontal Line Test; it's a straight line with a non-zero slope, so each horizontal line intersects the graph at exactly one point.
D. p(x) = |x| - Although this function is continuous and passes through the origin, it fails the Horizontal Line Test for values of x other than 0 because horizontal lines above and below the x-axis intersect the graph at two points each.
Thus, the correct answer is C. m(x) = –7x, as this linear function has an inverse that is a function.